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What Skills Should a Teacher of Mathematics Teach His/Her Students?
Before the advent of universal secondary education, the mathematics teacher had a select group of students who were most likely, in terms of Gardner’s multiple intelligences, mathematicallogical thinkers. So there was really no need for the math teacher to change the pedagogue away from “chalk and talk” and lots of drill practice.
But the second half of the 20th century saw most students progress through secondary schools. Soon most of the students were continuing their secondary education and most continued to study mathematics. This meant that these students had a variety of learning styles that we could equate to Gardner’s multiple intelligences.
This meant that math teachers needed to broaden their pedagogy and teach new skills to help all students in their mathematical development. At that time, I was the head of a math department at a large school introducing new curricula designed to bring math education into a position where it could cater to these different learning styles.
The content of the program is being modernized. The use of computers, scientific and graphing calculators and the Internet has become mandatory. This got me thinking about what additional skills my students needed to develop. Other teachers of other subjects most likely wanted to develop them as well.
Another school’s request for me to explain how my department coped with the shift from 40minute to 70minute periods got me thinking about these skills. I discussed my list and got its acceptance during the workshop.
Below is a list of additional skills that I think we math teachers should strive to develop as soon as possible. (A short explanation may be included with each skill.)
They are:

Communication skills. One aspect of some new programs is the introduction of problems in unfamiliar contexts that require the solutions to be fully communicated.

Calculator skills. The calculator allows the student to quickly perform the necessary calculations. Students should learn to check and estimate to facilitate their correct use. Graphing calculators have builtin programs that delve into reallife problems.

Computer skills.

Internet skills.

Skills to concentrate effectively in class. This is important because there is less time allocated to teaching mathematics than in the past. This should incorporate skills on how to be a powerful listener.

Textbook skills. This is the student’s first option in consolidating classroom learning. The student must know how to best use it.

Homework and study skills.

Exam skills, including how to solve a problem and how to develop an exam technique that helps ensure the best results.

Problem solving/critical thinking skills. And

In high school where life becomes extremely busy, organizational skills.
These skills cannot be developed overnight. All mathematics teachers must commit to introducing them from the first day of a student’s life in secondary school, whenever the opportunity arises. Separate skill lessons are not the best options. Dropping different skill ideas into daily lessons is a better option since the student will see it in a daily event, not contrived.
What I’ve suggested here in many ways is a “wish list”. If all math teachers embrace the need for these skills, they will gradually, over time, become a natural part of the student’s mathematical personality.
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